What is the domain and range of arctan?

Domain: all real numbers. Range: (−90°, 90°) or (−π/2, π/2) radians.

Why does arctan have a larger domain than arcsin and arccos?

Tangent is defined for all angles except ±90°, so its inverse also accepts all real values.

atan2(y, x) takes two arguments and returns the angle in the correct quadrant. arctan only uses one value.

Mathematics

Value (must be in [−1, 1] for sin/cos)

Arctan (inverse tangent, tan⁻¹) returns the angle whose tangent equals the input. Unlike arcsin and arccos, the domain is all real numbers (−∞, +∞).

Symbol	Name	Unit	Description
x	input value (tangent)	—	any real number (−∞, +∞)
θ	angle result	degrees or radians	—

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Inverse tangent - find angle from tan value. Formula, variable legend, diagram and worked example included. Instant geometry result.

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